1. Field of the Invention
This invention relates to systems and methods for measuring gas flow and in particular, for determining with high accuracy the supercompressibility factor, from which an indication of gas volume at base conditions may be calculated.
2. State of the Prior Art
In the past several years, the costs of all energy forms, first petroleum and other fuels such as natural gas, have risen drastically. Further, as supplies of petroleum, and in particular, imported petroleum, have dwindled, there has been a necessary reliance upon the supply of natural gas that is domestically available. Typically, such natural gas is transmitted via pipelines over great distances where the temperature and pressure conditions vary. For example, at the point of transmission the pressure may be in the range of 800-1,200 psi, whereas at an intermediate distributor, the pressure may be reduced to be in the order of 100-300 psi. At the level of distribution that would take place in a city, the pressure is still further reduced to a level in the order of 15 psi, whereas at the ultimate customer's home, the pressure may be in the order of 0.25 psi. Similarly, the temperature to which the gas is subjected may vary in the range of 0.degree. to 50.degree. C.
To distribute and sell gas that is exposed to these varying conditions, calculations must be made to convert the measured gas flow V.sub.f in terms of cubic feet at varying conditions of temperature T.sub.f and pressure P.sub.f, to a standard cubic feet volume V.sub.b at specified, previously-agreed-upon base temperatures T.sub.b and base pressure P.sub.b. To translate the measured volume V.sub.f of the flowing gas to the volume V.sub.b, it is customary to apply the ideal gas equation, given as follows: ##EQU1## where EQU P.sub.F =P.sub.f +Atmos. Pressure Base, and EQU T.sub.F =T.sub.f +459.67.
As seen from equation (1), all gases vary in volume directly proportional to temperature and inversely proportional to pressure. Additionally and significantly, the translated or base volume V.sub.b also is a function of the supercompressibility factor S, this factor being of increasing significance at pressures above 50 psi.
The supercompressibility factor S is rather complicated to calculate, as will be seen below, since it is a function of three primary variables: pressure, temperature and specific gravity. The factor S is also a function of the composition of the gas being measured, in terms of mole percents of the gases such as nitrogen and carbon dioxide. Due to the complexity of this function, equipment has not been developed to automatically make the supercompressibility correction in the computation of the quantity of the flow of gas V.sub.b. In some applications, it is possible to program an average value of the supercompressibility factor into a flow computer. However, where the pressure, temperature and specific gravity vary over a wide range, such an average factor is not particularly useful. Though a flow computer could normally be used in many applications, it will not because of an inability to provide an accurate indication of gas flow V.sub.b because of the difficulty to calculate the supercompressibility factor S.
The calculations for determining the supercompressibility factor S are given as follows: ##EQU2## EQU K.sub.t =M.sub.c +1.681 M.sub.n, (4)
where
M.sub.c is mole(s) of CO.sub.2 and PA1 M.sub.n is mole(s) of N. ##EQU3## where G is specific gravity. ##EQU4## where t is measured line temperature EQU K.sub.p =M.sub.c -0.392 M.sub.n ( 6) ##EQU5## where P is measured line pressure ##EQU6## Equation 14 is valid for pressure ranges of 0-1300 psi and a temperature range of -40.degree. F.+85.degree. F., where T.sub.f is the flow temperature, P.sub.f is the flow pressure, G is the specific gravity of the gas being measured, M.sub.c is the percent mole concentration of the CO.sub.2 component of the gas, and M.sub.n is the percent mole concentration of the nitrogen in the gas. Thus, it can be seen that it is quite complex to make an accurate determination of the supercompressibility factor S.
To more fully appreciate the nature of these measurements, reference is made to FIG. 1, wherein there is shown a conduit 10 through which natural gas is transmitted from a source to the ultimate user. Typically, the natural gas is made up of methane, ethane, propane and other components such as carbon dioxide and nitrogen, having specific percent moles thereof. The gas flow in terms of volume is metered by a gas turbine meter 12 having a rotor 13 that rotates as the gas flows through the meter 12 and exerts force on the blades of the rotor 13. A detector 14 detects the number of rotations of the rotor 13 and provides a series of discrete pulses via conductor 16 to a gas flow computer 30. The number of pulses generated by the detector 14 is an indication of the measured, uncorrected gas volume V.sub.f passing through the conduit 10. A static pressure transducer 20 monitors the pressure P.sub.f of the gas flowing in the conduit 10 as is supplied thereto through conduit 18, thereby to provide an output via conductor 22 to the computer 30 indicative of the measured pressure P.sub.f. Further, a temperature transducer 24 having a temperature probe 26 disposed within the conduit 10 measures the temperature T.sub.f of the flowing gas to provide an electrical signal indicative thereof along conduit 28 to the computer 30. As will be explained, the purpose of this invention is to calculate with a high degree of accuracy the adjusted flow in terms of standard cubic feet V.sub.b at standard pressure and temperature P.sub.b and T.sub.b. In the transmission and sale of natural gas, the factors such as standard pressure and temperature are contractually decided by the suppliers and distributors of natural gas. In keeping equation (1) to a form comparable to the gas laws, the uncorrected volume V.sub.f (cu. ft.) was inserted for the volume term. In a more detailed version, equation (1), V.sub.f =(K)(P) where P =Pulses and K=Cu. Ft./Pulse. The factor K as set out in equation (1) is a factor determined by the type of gas turbine meter 12 that is utilized.
The criticality of determining accurately the base or standard cubic feet V.sub.b, is more fully comprehended when the quantity and thus the cost of providing natural gas is considered. It is contemplated that in a large transmission line, including perhaps as many as 7 conduits, as much as 9 million standard cubic feet per hour per conduit of natural gas may be transmitted. In the last few years, the price of natural gas has risen from approximately 30 cents to $2.00 per cubic foot, as measured at standard base conditions. Thus, the value of a single day's transmission of gas along a single transmission line may be in the order of $200 million. Thus, the natural gas transmission companies are extremely interested in obtaining exceptionally accurate measurements to determine their contractual liability to the suppliers of natural gas as well as to transmit an accurate quantity of this gas to the ultimate user. Thus, it may be seen that even an increase in accuracy from 1% to 0.1% represents a considerable savings or loss, as the case may be, in the accurate sale and transmission of natural gas.
In the prior art, as illustrated by U.S. Pat. No. 3,537,312, flow measurements are made of absolute temperature, absolute pressure and turbine flow to provide an indication of volume in base terms of units of weight. The noted patent does recognize the various errors in the calculating circuitry to obtain this base measurement and suggests the use of a diode function generator to compensate for pressure transducer errors in accordance with density/pressure/temperature curves obtained experimentally. This patent notes that the apparatus as a whole obtains an accuracy within +1% or -1%. As seen from the discussion above, an accuracy to within but 1% would present a potential loss in the order of millions of dollars, and thus it is desired to obtain measurements of even greater accuracy.
In U.S. Pat. No. 3,701,280, the problem of translating measured gas flow at measured flow temperature and flow pressure, to obtain standard cubic feet at base temperature and pressures, is discussed. In this patent, it is noted that the volume at base conditions does vary from the Ideal Gas Law, i.e., that gas will vary in volume as a function of temperature and inversely as a function of pressure, by a deviation factor, i.e., the supercompressibility factor S. This patent goes on to note that it is quite complex to compute the supercompressibility factor and instead suggests that various predetermined functions of pressure, temperature and specific gravity may be used to calculate the deviation, i.e., the deviation with the supercompressibility factor S. In particular, these functions that are used to determine the supercompressibility factor S are approximated over limited, preselected ranges of pressure, of temperature and of specific gravity by taking values from the "Manual for Determination of Supercompressibility Factors for Natural Gas", PAR Research Projects NX-19, published by the American Gas Association, and using these values to determine the noted functions of temperature, pressure and gas. However, it is significant that such calculations are approximations and do not attempt to calculate specifically the exact values of the supercompressibility factor S in accordance with the equations (2) to (14) as set out above. This patent is illustrative of the current state of the art, wherein more sophisticated calculation techniques are used to obtain estimates of the supercompressibility factors and the overall accuracy of the calculations of the standard cubic feet V.sub.b of natural gas have been in the order of 0.1%.